Objective modeling of strain localization

ABSTRACT. This paper provides an elementary introduction into modeling of localized inelastic processes such as cracking or formation of shear bands. The basic concepts are explained using a simple one-dimensional example. It is shown that a stress-strain law with softening used in a standard continuum description leads to physically meaningless results and that the numerical solution suffers by a pathological sensitivity to the finite element discretization. The paper presents an overview of methods that provide an objective description of the localization problem. Regularization techniques are illustrated by examples dealing with the nonlocal damage model and with the softening plasticity model enhanced by the second gradient of the cumulative plastic strain.